Aste T., Weaire D. Pursuit of perfect packing (IOP 2000)(147s).pdf
Aste T., Weaire D. Pursuit of perfect packing (IOP 2000)(147s).pdf
Aste T., Weaire D. Pursuit of perfect packing (IOP 2000)(147s).pdf
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18 Loose change and tight <strong>packing</strong><br />
(a)<br />
(b)<br />
Figure 2.13. Two examples <strong>of</strong> fractal <strong>packing</strong>s: the Apollonian <strong>packing</strong> (a), the loxodromic<br />
sequence <strong>of</strong> circles (b). (See Coxeter H S I 1966 Loxodromic sequences <strong>of</strong> tangent<br />
spheres AEQ. MATH 1 104–21.)<br />
1908) but the primary credit probably belongs to Dirichlet, in 1850. Both he and<br />
Voronoï used the construction for a rather abstract mathematical purpose in the<br />
study <strong>of</strong> quadratic forms. Since then, it has played a supporting role in many<br />
important theories.<br />
The modern use <strong>of</strong> Voronoï diagrams in physical science (in two, three or in<br />
many dimensions) began with crystallography but has since become much more<br />
general. In geography and ecology, indeed everywhere that spatial patterns are
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